Is ekiri more "start going" like start leaving a party and saying goodbye to everyone, or "Unfortunately, I need to start going to class". The ek makes me think ekster so more in line with the first one.
The first one. The ek prefix means to start to do something or to suddenly do something.
Isn't "ekiri" "to go out"? I would have thought "to go" would be "iri."
Yeah, now that I have done the rest of the lesson, I realize that we were misled by our acquaintance with Latin. Usually, it is safe to assume that Mr Zamenhof pinched his Esperanto words from Latin (or English), but not here, I guess.
Dr Zamenhof did take a lot (though by no means everything) from Latin, sometimes using slightly different forms in order to create distinctions which Latin lacked.